Hi there and welcome to our community!
To answer your questions as simply as I can:
Mining is the process of verifying transactions on the network, and in doing so, being rewarded with Feathercoins. Each new block of transactions has a puzzle that needs to be solved. This puzzle requires a lot of computer power to solve, it would be impossible to figure out by a person with a calculator in a single lifetime. The first miner to successfully solve the puzzle gets 200 coins. Their block gets added onto to the blockchain, which is like adding a new page to a ledger. Except the ledger is public, so you can always verify each transaction you’ve made.
The miners are like the bank. Or Visa/Mastercard. They process transactions and secure the network. This isn’t the best analogy, but you can think of it like that for simplicity.
Merchants on the other hand don’t need to worry so much about the technical side of things. Because mining is the part that’s dealing with the blockchain - whereas Merchants are more interested in dealing with the currency side of the system, the Feathercoins.
Right now to become a merchant that accepts Feathercoin, you have several options. One, you can use a system like CoinPayments - which simplifies the process for you, but charges a fee. You can place things on our Marketplace, and also for a small fee can have the service provide the legwork for you. Or, you can deal with each customer directly - once an order for FTC goes through, you can email them with an FTC address [you generate these in the wallet software] and ask them to send their Feathercoin there. Once you verify the payment, you can contact the buyer and ship your product out. Unlike credit cards, there is no possibility of chargebacks. So the buyer would have to trust that you have shipped out [you can do this by sending a tracking number].
Using a third-party system like CoinPayments or the Market makes the transactions a bit more secure. They can act as escrow for the sales.
Hope that was good enough!